Search

The launch of gravity-dedicated satellite missions at the beginning of the new millennium led to an accuracy improvement of global Earth gravity field models (GGMs). One of these missions was the Gravity field and steady-state Ocean Circulation Explorer (GOCE) launched in 2009. As the first European Space Agency's Earth Explorer Mission, the satellite carried a novel instrument, a 3-D gradiometer, which allowed measurement of the second-order directional derivatives of the gravitational potential (gravitational gradients) with a uniform quality and a near-global coverage. The main mission goal was to determine the static Earth's gravity field with the ambitious precision of 1-2 cm in terms of geoid heights and 1 mGal in terms of gravity anomalies for spatial resolution of 100 km (half wavelength at the equator). More than three years of the outstanding measurements resulted in three levels of data products (Level 0, Level 1b and Level 2), six releases of GGMs, and several global grids of gravitational gradients. The grids, which represent a step between gravitational gradients measured directly along the GOCE orbit and those represented by GGMs, found their usage mainly in geophysical applications. In this contribution, we validate the official Level 2 product GRD_SPW_2 using height anomalies over two test areas located in central and northern Europe (Czechia/Slovakia and Norway). A mathematical model based on the least-squares spectral weighting is employed with corresponding spectral weights estimated for validation of gravitational gradient grids. This model continues gravitational gradients from the mean orbital altitude of GOCE down to the irregular Earth's surface (not to a sphere) and transforms them to height anomalies in one computational step. Analytical downward continuation errors of the model are estimated using a closed-loop test. Prior to the comparison of height anomalies estimated from gravitational gradients with their reference values derived from Global Navigation Satellite Systems (GNSS)/levelling over the two test areas, the gravitational gradients and reference data are corrected for all systematic effects such as the tide system conversion. Moreover, the high-frequency part of the gravitational signal is estimated and subtracted from reference data as it is attenuated in the gravitational gradients measured by GOCE. A relative improvement between the release 6 and release 2 gradient grids reaches 48 % in terms of height anomalies in Czechia/Slovakia. The relative improvement in Norway is even more significant and reaches 55 % . The release 6 of the official Level 2 product GRD_SPW_2 gained the absolute accuracy with the standard deviation of 8.7 cm over Czechia/Slovakia and 9.3 cm over Norway. Article Highlights: A mathematical model based on the least-squares spectral weighting for validation of the official Level 2 product GRD_SPW_2 is presented Possibilities of the spectral combination method for the downward continuation of gravitational gradients and their transformation into height anomalies are investigated A review of quality of the official Level 2 product GRD_SPW_2 with respect to GNSS/levelling points over two test areas (Czechia/Slovakia and Norway) is provided [ABSTRACT FROM AUTHOR]

Downward continuation of the potential data (gravity or magnetic) helps to interpret contributing sources by transforming the physical signal to their neighborhood. This paper applies three continuation approaches (Landweber's iteration, the direct method and the inverse-matrix approach with Tikhonov's regularization), based on the Poisson integral equation, and four integration schemes to the second vertical derivative of the anomalous potential $$T_{\rm zz}$$ obtained from GOCE data. In the experiments, $$T_{\rm zz}$$ was downward continued for 250 km in the area of Central Europe with special attention to edge effects. For the integration schemes, which use prior information outside the region of interest to reduce edge effects, the best agreement with TIM-r4 was achieved by the inverse-matrix approach with Tikhonov's regularization (RMS = 1.15 eotvos). On the contrary, without prior information the iterative approach performed with RMS = 1.17 eotvos. [ABSTRACT FROM AUTHOR]

In the last few decades, satellites have acquired various potential data sets hundreds of kilometers above the Earth's surface. Conventionally, these global magnetic and gravitational data sets are approximated by using spherical harmonics that allow straightforward work with both fields outside the Earth's mass. In this article, we present an alternative approach for working with potential data in mass-free space given over a regular coordinate grid on a spherical surface. The algorithm is based on an iterative scheme and the Poisson integral equation for the sphere. With help from the Fourier transform, global potential (magnetic or gravitational) data can efficiently be continued from a mean orbital sphere down to a reference surface without using the spherical harmonics. This is illustrated both with simulated magnetic field data and with real data from the satellite gradiometry mission GOCE. In the case of simulated magnetic data and the downward continuation for 450 km, we have achieved a root mean square at the level of 0.05 nT, while it was <1 E (eotvos) for real GOCE data continued for 250 km. The crucial point is to apply the algorithm twice as a large part of noise can be removed from the input data. [ABSTRACT FROM AUTHOR]